Lecture 1: Course Overview and Review of Institutions and Markets

The goals of this class

Understand important financial institutions and markets
Provide a toolkit for creating portfolios of financial assets
Use asset pricing models to understand the trade-off between risk and return
Apply these models to:
1. identify investment opportunities
2. evaluate portfolio performance

Who am I?

Former research economist at the Federal Reserve Bank of New York (2015-2018)
PhD in economics at Harvard from 2009-2015
Research associate at the FRBNY (2007-2009)

Main research focus:
1. Consumer finance – bankruptcy, mortgages, housing
2. Applied statistics – machine learning and other methods
Email: paul.goldsmith-pinkham@yale.edu
- Please reach out if you have any concerns or questions re: policy that are not laid out in the syllabus.
Website: http://paulgp.github.io
Office: 4532

Timeline for our course

Part 1: Institutional details

Who are the buyers and issuers of financial instruments?
Define assets + securities classes
How are financial assets traded?
How have these financial assets performed historically?
- Strong focus on statistical properties and data

Timeline for our course

Part 2: Portfolio tools

How do we interpret observed returns?
- Build to a model of returns
Three ingredients necessary for our models:
1. Defining risk appetite/aversion
2. Understanding mean‐variance trade-off
3. Allocating between risky and safe investments
Use models to construct a portfolio of risky investments
- Capital Asset Pricing Model
- Arbitrage Pricing Theory / Factor Models

Timeline for our course

Part 3: Critical evaluation of the tools

How consistent is CAPM with the data?
How should we use the models when there are market anomalies?
- Active portfolio management
- Treynor-Black / Black-Litterman
- Robust Portfolio Management

Timeline for our course

Part 4: Evaluate and attribute portfolio returns

CAPM / APT describe returns from a passive strategy (no skill required)
How should we evaluate active managers?
- Portfolio evaluation techniques answers:
  “Did you beat your benchmark?”
- Performance attribution answers the question,
  “How did you beat your benchmark?”

Timeline for our course

Part 5: Applications and alternative forms of investing

Private equity and hedge funds
Fixed income (bonds, futures, forwards)

Class requirements

Straight from the syllabus!
Three problem sets as homework:
- Due April 4, April 12 and May 7
- To be done individually
Two case write-ups:
- Yale University Investments Office \ (Due in class April 16)
- Firefighter (Due in class April 28)
- To be done in groups 3-5
- Subject to change

Section TA: David Kwon

Institutions

Global assets under management

Institutions

U.S. Institutional Holdings

Institutions

Mutual Funds

Also known as open-end funds
- Investors pool and benefit from sharing information
  collection and back‐office costs
Fund issues new shares when investors buy in and redeems shares when investors cash out
Priced at Net Asset Value (NAV):

\[ \frac{\text{Market Value of Assets} - \text{Liabilities}}{\text{Shares Outstanding}} \]

Institutions

Mutual Funds Fees

Fee Structure: Four types
1. Operating expenses (recurring)
2. 12 b‐1 charge (recurring)
3. Front‐end load (one time)
4. Back‐end load (one time)
Fees must be disclosed in the prospectus
Share classes with different fee combinations

Institutions

Example of fees for various classes of mutual funds

Compare the A, B and C shares
What are the trade-offs between initial and deferred loads?
Level of annual fees and expenses

Mutual Funds - fees and incentives

People don’t avoid high-fee index funds (Choi et al. 2010)
Experimenters overfocused on returns since fund inception

Mutual Funds - fees and incentives

Fund flow response distorts risk-taking incentives (Chevalier and Ellison (1997))

Mutual Funds - costs over time

Mutual fund expense ratios have fallen over time, driven by several factors

Scale economies - assets under management have grown
Competition - investors pick funds with lower expense ratios
Increased presence of employer-sponsored retirement plans

Source: Investment Company Institute

Do mutual fund managers earn their fees?

How could we answer this?

One idea: how do mutual funds do compared to an index?

Performance of actively managed funds below the return on:
- the Wilshire index in 23 of the 39 years from 1971 to 2009
- the S&P index in 30 of the 47 years from 1970 to 2017

Institutions

Mutual Funds - do fund managers earn their fees?

Are all mutual fund managers like Andy Dwyer, or just the average?
Malkiel (1995) evaluates 239 mutual funds with at least ten-year records
- Compare each fund’s performance to holding the S&P 500

Institutions

Is there a “hot hand” for mutual fund managers?

Evidence for persistent performance is weak, but suggestive
Malkiel (1995) tracks funds based on above/below median performance:

Institutions

Mutual Funds – Persistence in performance?

Bollen and Busse (2004) find tiny persistence at the quarterly level

Institutions

What else? Other buyers/Other perspectives

Closed-end funds (small now)
Pension funds
Endowment Funds
Alternative Asset Managers
- to be discussed in the context of cases and guest lectures
Next up…market structure

Market Structure

What kinds of markets are there?

Specialist Markets
Over-the-counter (OTC) markets
Electronic Communication Markets

Market Structure

What types of orders are there?

Market order – Buy or sell order to be executed immediately at prevailing bid/ask price
Limit order – Buy or sell order with a pre‐specified limit for the price

Limit orders make up a limit order book

Market Structure

Types of Markets: Specialist Exchanges

Example of a specialist exchange: NYSE
Trading traditionally occurred through a combination of an auction (the order book) and a market maker (the specialist)
Orders sent to exchange may be cleared electronically or sent to specialist
- Only one specialist for each stock
- Specialist may act as broker or as a dealer

Market Structure

Roles of specialists in specialist exchanges

Broker
- Matches buy and sell orders
- Income generated by commissions
Dealer
- Specialists maintain their own bid and ask quotes and fill orders with own account if market spread too high
- Historically, participated in about 25% of all transactions
- Maintained price continuity

Market Structure

Types of Markets: OTC Markets

Trades negotiated dealer‐to‐dealer
Nasdaq (National Association of Securities Dealers Automated Quotation system)
- Originally, a price quotation system
- Large orders may still be negotiated through brokers and dealers
- Today, NASDAQ provides electronic trading (less OTC)

Market Structure

Types of Markets: Electronic Communication Networks

Private computer networks that directly link buyers with sellers for automated order execution
To attract liquidity, networks may pay rebates to liquidity providers (market makers)
Electronic clearing facilitates high frequency trading

Market Structure

Short-selling

In our optimal portfolio, we’ll have the option to “short”–sell stocks that we don’t own
Why would we?
1. Stock may be overpriced (negative alpha)
2. Stock may be appropriately priced, but we want to hedge out risk from a long position in a similar security (pairs trading)
So what is it?

Market Structure

Short-selling Mechanics

Suppose we have one dollar and believe stock A will underperform stock B.

Buy $1 of asset B
Borrow $1 worth of stock A ( $1 \big/ P_A$ shares) and promptly sell the stock
- Now, you owe the owner of A his shares back and will have to repurchase them in the market at tomorrow’s price
- Proceeds from the sale serve as collateral to stock lender (e.g. $1)
- Reg T requires 50% additional collateral (above and beyond proceeds) be kept in account (shares of B will suffice)

\[\text{Final Payoff} = 1 + (r_B ‐ r_A) + \ldots+ \underbrace{\text{short rebate}}_{\text{to be defined}}\]

Market Structure

Short-selling Mechanics

Assume that $P_{A} = 100$, and you want to short the stock. What will your return be if the stock drops to $P_{A} = 25$?
First, calculate your initial position:
1. You will borrow a share of stock A and sell it immediately. You now have $100 dollars, but owe 1 share of Stock A.
2. You addditionally post the required 50% collateral (e.g. $50 of a treasury bill)

Assets	Liabilities
Cash 100	Short position 100
T-Bill Collateral 50	Equity 50

Now imagine the stock drops to $P_{A}$ = 25 and you close your position:
1. You buy the stock at $25, and return it to the original owner
2. The collateral and cash are returned to you, net of your purchase
As a result, you have 75 dollars profit. Your return is $r_{\text{short}} = \frac{75}{150} = 0.50$
Note that the maximum upside is a return of 66.6%. Why? Because the initial sale at 100$ creates a liability of $100 dollars – at best, this liability goes to zero, netting 100 dollars in profit and a return of 66% given the need to post 150 dollars in collateral.
- Note that the downside is unlimited.
- In many cases, the dynamics matter: if market moves against you, you will need to put more collateral in.
- Keynes: “Markets can stay irrational longer than you can stay solvent.”

Market Structure

Short-selling Mechanics

Now assume we do this in pairs. There are two stocks, $A$ and $B$, each worth 100 dollars.We buy stock $B$ and short stock $A$. What will your return be if next period, $P_{A} = 90$ and $P_{B} = 105$?
First, calculate your initial position:
1. You will borrow a share of stock A and sell it immediately. You now have $100 dollars, but owe 1 share of Stock A.
2. You addditionally post the required 50% collateral (you can post stock $B$ shares)

Assets	Liabilities
Cash 100	Short position 100
Stock B Collateral 50	Equity 100
Stock B 50

Now imagine the stocks change to $P_{A} = 90$ and $P_{B} = 105$ and you close your position:
1. You buy the stock at $90, and return it to the original owner
2. The collateral and cash are returned to you, net of your purchase
3. You sell Stock B at $105
As a result, you have 10 dollars profit from stock A and 5 dollars profit from stock B.
- Your returns are $r_{\text{short}} = -r_{A} = 0.1$ and $r_{\text{long}} = r_{B}$ = 0.05
- Our total profit is 15 dollars. Our net return is ((100 - 90) + (105 - 100))/200 =0.075.

Market Structure

What is the short rebate?

Short rebate is the interest I earn on my dollar of collateral sitting with the stock lender

\[ \text{Short Rebate} = r_{f} - \text{Security lending Fee} \]

Securities lending fees vary greatly and reflect how easy the shares are to borrow (often less than 20 bps)
In obvious shorting situations, short rebate will go negative (shares “hot or trading “special”) or can’t be found

Lecture 2: Risk and Return

Measuring Assets’ Returns

Let’s begin by focusing on two major asset classes - stocks and bonds
How have these assets performed historically?
- What’s the best way to summarize their risk + return?

Measuring Assets’ Returns

Why does a Treasury bill’s return not fall below zero?
Is monthly return the best measure? What else could we do?
- Let’s quickly refresh ourselves on how to measure returns.

Return Definitions

“Return” A.K.A. rate of return A.K.A. net return
\[ r_{t} = \frac{P_{t} + D_{t}}{P_{t-1}} - 1 \]
Gross returns (sometimes $R_{t}$) referred to as $1+r_{t}$
The risk-free rate will be called $r_{f}$
- How can I get the risk-free rate?
Excess returns above the risk free rate are $r_{e} = r - r_{f}$

Return Defintions

A holding-period return of $T$ years is

\[ r_{0,T} = (1+r_{1})(1+r_{2})\ldots (1+r_{T}) - 1 \]

How you measure the holding period matters a ton!
Recall the mutual fund experiment

Return Definitions

How do we compare returns across different horizons?
- Say I want to compare a window of cumulative returns 5 v 10 years.

Annualized returns on the cumulative return: \[ \widetilde{r}_{0,T} = (1+r_{0,T})^{\frac{1}{T_{\text{years}}}} - 1 \]

Return Definitions

Arithmetic average returns \[ \overline{r} = \frac{1}{T}(r_{1} + r_{2} + \ldots + r_{T}) \]
Geometric average returns \[ r_{G} = \left[(1+r_{1})(1+r_{1})\ldots (1+r_{T})\right]^{\frac{1}{T}} - 1 = \big[\frac{P_{T}}{P_{0}}\big]^{\frac{1}{T}} - 1 \]
- Arithmetic average is unbiased estimate of 1-period future returns (expected returns)
- Geometric average is a measure of cumulative past performance

Return Definitions

We calculate estimates of variance using squared deviations from arithmetic average returns \[ \sigma^{2}(r) = VAR(r) = \frac{1}{T}\bigg((r_{1}-\overline{r})^{2} + (r_{2}-\overline{r})^{2} + \ldots + (r_{T}-\overline{r})^{2})\bigg) \]
Standard deviation is the square-root of variance: \[ \sigma(r) = SD(r) = \sqrt{\frac{1}{T}\bigg((r_{1}-\overline{r})^{2} + (r_{2}-\overline{r})^{2} + \ldots + (r_{T}-\overline{r})^{2})\bigg)} \]

Return Defintions

Finally, covariance measures how two returns move together \[ \begin{aligned} \sigma_{i,j} = COV(r_{i}, r_{j}) = \frac{1}{T}\bigg((r_{1,i}-\overline{r}_{i})(r_{1,j}-\overline{r}_{j}) &+ (r_{2,i}-\overline{r}_{i})(r_{2,j}-\overline{r}_{j})\\ &+ \ldots + (r_{T,i}-\overline{r}_{i})(r_{T,j}-\overline{r}_{j})\bigg) \end{aligned} \]
Correlations scale the covariance by standard deviations \[ \rho_{i,j} = \frac{\sigma_{i,j}}{\sigma_{i}\sigma_{j}} \]
Excel provides functions AVERAGE,GEOMEAN,VAR, STDEV, and COVAR

Wanted: Information about risk and return

To make investment decisions, we need to know
- … the expected future returns
- … the riskiness of future returns
We turn to historical return data for these
- A caveat…
- The data give a pretty good sense of the risk, but expected returns are hard to measure.
- Why?

Asset Returns: Historical Record

United States

Siegel (1992) provides average real return data for the U.S. since 1802:

Historical Returns from Siegel (1992)
	Stocks			Bonds
Period	Arithmetic Mean	Arithmetic SD	Geometric Mean	Arithmetic Mean	Arithmetic SD	Geometric Mean
1802-1990	7.80	18.40	6.2	3.1	6.20	2.90
1802-1870	6.90	16.60	5.7	5.4	7.60	5.10
1871-1925	7.90	16.60	6.6	3.3	4.80	3.10
1925-1990	8.60	21.20	6.4	0.6	4.30	0.50
1990-	9.03	18.78	7.3	0.4	2.12	0.38

Historic variation in risk premium (stocks minus bonds)
Stock returns are remarkably strong. Is US an outlier?

Asset Returns: Historical Record

US returns high, but not an outlier

Asset Returns: Historical Record

Average s.d. of returns is 23% (US 20%)
What’s up with Italy, Germany, Japan?

High returns or survivorship bias?

Countries with low returns fall out of the analysis (Jorion and Goetzmann (1999)).
Median real return of all other countries is 0.75% (compared to 4.3% for US).

Still waiting for data?

Most recent U.S. historical data suggest:

Average excess returns of large stocks over long term bonds ($r_{e}$) of roughly 6% … with a standard deviation of 20% ($\sigma_{e}$)
With 81 years of data, standard error associated with mean excess returns is \[ \sigma(\overline{r}_{e}) = \frac{\sigma(r_{e})}{\sqrt{T}} = \frac{20 \%}{9} \approx 2.2\% \]
Can we reject the null hypothesis that excess returns are 4%… or 2%?

How can we forecast returns going forward?

Recall that

\[ r_{1} = \underbrace{\frac{D_{1}}{P_{0}}}_{\text{dividend yield}} + \underbrace{\frac{P_{1}}{P_{0}}}_{\text{growth}} \]

Also,

\[ \underbrace{\frac{D_{1}}{P_{0}}}_{\text{dividend yield}} = \text{earnings payout share} \times \frac{E_{1}}{P_{0}} \] where, $E_{1}$ is earnings.

This implies \[ r_{1} = \text{firm's payout share} \times \frac{E_{1}}{P_{0}} + \text{growth} \]

The Gordon Model

\[ r_{1} = \text{payout share} \times \frac{E_{1}}{P_{0}} + \text{growth} \]

Historically, payout has been around 50%, P/E about 25 and growth rate of about 4-5% (nominal)
- What does that imply about nominal expected returns?

Estimate is about 6-7% nominal expected return for stocks, or 4% real, or a risk premium of 2-3% over nominal bonds
This is very low versus history
To believe anything else, you must disagree with payout, E/P, or growth.

Shiller Price-Earnings Ratios

Takeaways

We still have a limited amount of high quality data to make inferences from, but…
Historical data suggests a premium for risk in asset returns, but the size of the premium is up for debate
If expected returns for the aggregate stock market with 80+ years of data are so imprecise, what are we to do with individual stocks?
Need more than data to understand expected returns

Other risk measures

Value at Risk (VaR)

A measure of loss most frequently associated with extreme negative returns
VaR is the quantile of a distribution below which lies q % of the possible values of that distribution
The 5% VaR, commonly estimated in practice, tells us how bad returns (or losses) will be in the worst 5% of times

VaR under normality

5% VaR return is equal to E(r) - 1.645 X s.d.
- 5% Value at Risk (VaR) represents the lower bound on the return’s 10% confidence interval
Under non-normality, look at historic returns for 5% cutoff

Expected Shortfall (ES)

Also called conditional tail expectation (CTE)
More conservative measure of downside risk than VaR
- VaR takes the highest return from the worst cases
- ES takes an average return of the worst cases